A data consists of $n$ observations

${x_1},{x_2},......,{x_n}.$ If $\sum\limits_{i - 1}^n {{{({x_i} + 1)}^2}}  = 9n$ and $\sum\limits_{i - 1}^n {{{({x_i} - 1)}^2}}  = 5n,$ then the standard deviation of this data is

The variance of the first $n$ natural numbers is

From a lot of $12$ items containing $3$ defectives, a sample of $5$ items is drawn at random. Let the random variable $\mathrm{X}$ denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If variance of $X$ is $\frac{m}{n}$, where $\operatorname{gcd}(m, n)=1$, then $n-m$ is equal to..........

Let $x_1, x_2, x_3, x_4, .......... , x_n$ be $n$ observations and let $\bar x$ be their arithmetic mean and $\sigma ^2$ be their variance.

Statement $-1$ : Variance of observations $2x_1, 2x_2, 2x_3, ......, 2x_n$ is $4\sigma ^2$ .

Statement $-2$ : Arithmetic mean of $2x _1, 2x_2, 2x_3, ......, 2x_n$ is $4\bar x$ .

For two data sets, each of size $5$, the variances are given to be $4$ and $5$ and the corresponding means are given to be $2$ and $4$, respectively. The variance of the combined data set is

The mean and standard deviation of $40$ observations are $30$ and $5$ respectively. It was noticed that two of these observations $12$ and $10$ were wrongly recorded. If $\sigma$ is the standard deviation of the data after omitting the two wrong observations from the data, then $38 \sigma^{2}$ is equal to$.........$